On spin \(L\)-functions for orthogonal groups
type: Item
instance of: scholarly article
title: On spin \(L\)-functions for orthogonal groups
zbMATH Open document ID: 0832.11020
DOI: 10.1215/S0012-7094-95-07723-0
author: David Ginzburg
published in: Duke Mathematical Journal
publication date: 1996-03-07T00:00:00Z
review text: Let \(G= GSO_{2n}\) over a number field. The dual group is \(G\text{Spin}_{2n} (\mathbb{C})\). Let \(r_n\) be the \(2^{n-1}\)-dimensional spin representation of this group. The analytic properties of the partial \(L\)- function \(L_S (\pi\otimes \chi, r_n)\) for \(\pi\) a generic cuspidal representation of \(G(\mathbb{A})\) are studied, using the Rankin-Selberg method, for \(n=5\) and \(n=6\) (these are the only cases in which the algebra of \(U\)-invariants in \(\mathbb{C} [V]\), \(V\)= space of \(r_n\), is a polynomial ring). For \(n=5\) the Rankin-Selberg integral is of Hecke type, for \(n=6\) it involves an Eisenstein series of \(GSp_6\).
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F66
zbMATH DE Number: 784720
zbMATH Keywords: spin representation
zbMATH Keywords: partial \(L\)-function
zbMATH Keywords: generic cuspidal representation
zbMATH Keywords: Rankin-Selberg integral
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 784720